ar X iv : h ep - p h / 03 06 06 4 v 2 9 D ec 2 00 3 Transmutation of Scale Dependence into Truncation Uncertainty via RG - Improvement of the R ( s ) Series

The arbitrariness in how the logarithm is defined within the QCD series for the inclusive electroproduction cross-section is shown to affect the summation to all orders in α s of leading and successively-subleading logarithms within that perturbative series, even though such summations largely eliminate the residual dependence of the original series on the arbitrary renormalization scale µ. However, given that the original (unim-proved) series is known to third-order in α s (µ), this logarithm ambiguity is shown not to enter the optimally improved summation-of-logarithms series until the term fourth-order in α s (s), where s is the physical center-of-mass energy squared. Consequently, the ambiguity in how the logarithm is defined is absorbable in the uncertainty associated with truncating the original perturbative series after its calculationally known terms.